Question

Ch 7 Q1

In the last quarter of​ 2007, a group of 64 mutual funds had a mean return of 2.4​% with a standard deviation of 5.5​%. If a normal model can be used to model​ them, what percent of the funds would you expect to be in each​ region? Use the​ 68-95-99.7 rule to approximate the probabilities rather than using technology to find the values more precisely. Be sure to draw a picture first.

​ a) Returns of −14.1​% or less	​ b) Returns of 2.4​% or more
​c) Returns between −3.1​% and 7.9​%	​d) Returns of more than 13.4​%

​a) The expected percentage of returns that are −14.1​% or less is _________________

​(Type an integer or a​ decimal.)

​b) The expected percentage of returns that are 2.4​% or more is __________________

​(Type an integer or a​ decimal.)

​c) The expected percentage of returns that are between −3.1​% and 7.9​% is ______________

​(Type an integer or a​ decimal.)

d) The expected percentage of returns that are 13.4​% or more is ___________________

​(Type an integer or a​ decimal.)

Please show all of the math. It won't help me if you don't show the work.

Thank you!

Answer 1

Answer)

According to 68-95-99.7 rule

Approximately, 68% of the data lies within 1 standard deviation.

And 95% of the data lies with in 2 standard deviation.

And 99.7% of the data lies with in 3 standard deviation.

Mean = 2.4%

Standard deviation = 5.5%

So, 68% lies between (2.4-5.5) and (2.4+5.5)

Between -3.1 and 7.9

95% lies in between (2.4 - (2*5.5)) and (2.4+(2*5.5))

Between -8.6 and 13.4

99.7% lies in between (2.4 - (3*5.5)) and (2.4+(3*5.5))

Between -14.1 and 18.9

A)

P(14% or less)

99.7% lies in between -14.1 and 18.8

And 0.03 left

Out of which 0.015 lies on both sides, above 18.8 and below -14.1

Therefore

P(14% or less) = 0.015%

B)

P(2.4% or more) = as the normal model is symmetrical in nature

Therefore on both the sides of the mean, there would be 50%

So, above 2.4%, there is 50%

So, P(2.4% or more) = 50%

C)

Between (-3.1 and 7.9)

= 68% (explaned aboved)

D) 13.4% or more

95% of the data lies in between -8.6 and 13.4

Therefore, above 13.4%

There would be 0.025%